LIE SYMMETRY, EXACT SOLUTIONS AND CONSERVATION LAWS OF SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

Abstract

In this paper, Lie symmetry analysis method is applied to spacetime fractional reaction-diffusion equations and diffusion-convection Boussinesq equations. The Lie symmetries for the governing equations are obtained and used to get group generators for reducing the space-time fractional partial differential equations(FPDEs) with Riemann-Liouville fractional derivative to space-time fractional ordinary differential equations(FODEs) with ErdélyiKober fractional derivative. Then the Laplace transformation and the power series methods are applied to derive explicit solutions for the reduced equations. Moreover, the conservation theorems and the generalization of the Noether operators are developed to acquire the conservation laws for the equations. Some figures for the obtained explicit solutions are also presented.